A planet has a mass of 5.71 × 1023 kg and a radius of 3.93 × 106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 61.8-kg person weigh on this planet?
To calculate the acceleration due to gravity on a planet, we can use the equation:
g = G * (M / R^2),
where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), M is the mass of the planet, and R is the radius of the planet.
(a) To find the acceleration due to gravity on this planet, we can substitute the given values into the equation:
M = 5.71 × 10^23 kg
R = 3.93 × 10^6 m
g = G * (M / R^2)
= 6.67430 × 10^-11 * (5.71 × 10^23 / (3.93 × 10^6)^2)
≈ 6.67430 × 10^-11 * (5.71 × 10^23 / (3.93 × 10^12))
≈ 9.75 m/s^2
Therefore, the acceleration due to gravity on this planet is approximately 9.75 m/s^2.
(b) To find out how much a 61.8-kg person would weigh on this planet, we can use the formula:
Weight = Mass * Acceleration due to gravity
Weight = 61.8 kg * 9.75 m/s^2
= 602.55 N
Therefore, a 61.8-kg person would weigh approximately 602.55 Newtons on this planet.